Generalized Floquet theory for stationary Schrödinger operators in one dimension

Floquet theory for ordinary differential operators with periodic coefficients is well known and fundamental to study the stability of solutions and spectral properties of the operators. Generalization of Floquet theory to differential operators with almost periodic or more random coefficients have been done by several authors, by applying C*-algebra theory, dynamical theory and probability theory. The purpose of this paper is to give a general point of view of Floquet theory using the Weylʹs functions systematically, which was initiated by Johnson-Moser.